The Brown-Erdős-Sós Conjecture in finite abelian groups

2019/01/28 by József Solymosi, Solymosi, Jozsef, Ching Wong +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1901.09871

openalex publication_date 2019/01/28 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The Brown-Erdős-Sós conjecture, one of the central conjectures in extremal combinatorics, states that for any integer m≥ 6, if a 3-uniform hypergraph on n vertices contains no m vertices spanning at least m-3 edges, then the number of edges is o(n²). We prove the conjecture for triple systems coming from finite abelian groups.

Citations

• On a conjecture of Erdős on locally sparse Steiner triple systems

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